Starting with polynomial:
P : -t+1
Extension levels are: 1 3 19
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 19 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^23 + 2967417930088458284793920705351744450134437385517518486007649977219/6516696794286640554149519379353965622932972151062076330124068388*t^22 - 1229686618426373418405591750115990203393835737337757494933291553427943/13033393588573281108299038758707931245865944302124152660248136776*t^21 + 102591227810103949316497086752565608921968483882954472019250772937882693/8688929059048854072199359172471954163910629534749435106832091184*t^20 - 173612109082809906867474056365723517875360088178866561566927453212283977971/173778581180977081443987183449439083278212590694988702136641823680*t^19 + 10537145889916617549701781997203552369445654465051600878473626514879511357131/173778581180977081443987183449439083278212590694988702136641823680*t^18 - 237497270090730416900635635214580080644494865724467564390539510404655088084411/86889290590488540721993591724719541639106295347494351068320911840*t^17 + 477893397154711492415990111444729864325580547974547070816938153349123728473929/5111134740616972983646681866159973037594487961617314768724759520*t^16 - 392797899936864696523841703804651894608851010536452628994840823130909932087858/159722960644280405738958808317499157424827748800541086522648735*t^15 + 1600460976863212326688812048626422191350968169038293617817260290178944009141122/31944592128856081147791761663499831484965549760108217304529747*t^14 - 25328711086719656252436265461345516633898712635390513152076398654462218514654252/31944592128856081147791761663499831484965549760108217304529747*t^13 + 311140239764754145814211126465869055757672202011374697419708713339057930589861684/31944592128856081147791761663499831484965549760108217304529747*t^12 - 2954331488756585760718724027274410445920650081168238517230352536500269781371188712/31944592128856081147791761663499831484965549760108217304529747*t^11 + 21520726336290364407799157769978492804449929427873125388280269122156495469633473128/31944592128856081147791761663499831484965549760108217304529747*t^10 - 118944172133774533134540914678772742514770208562664776294451543727562623650180619280/31944592128856081147791761663499831484965549760108217304529747*t^9 + 491321048218506520362979076129788598651852534638090320010259690746767180492354488880/31944592128856081147791761663499831484965549760108217304529747*t^8 - 1486869467552972877686664738383033467397988598657171894910559856718880343412498223360/31944592128856081147791761663499831484965549760108217304529747*t^7 + 3211786555569535566125012341478532233073901303580665527400932432787726513703557121280/31944592128856081147791761663499831484965549760108217304529747*t^6 - 4784612329546696298890638669805476042044198601658611803314727766542442417807793374720/31944592128856081147791761663499831484965549760108217304529747*t^5 + 4691057769678147436833494847041624642128008839193185156174111957556053821701920371200/31944592128856081147791761663499831484965549760108217304529747*t^4 - 2829565114093491765099781138690384868457822426220384568390613515431222724130491251200/31944592128856081147791761663499831484965549760108217304529747*t^3 + 941963074310698216091183004562275144493158130964800822461570521492641978641151142400/31944592128856081147791761663499831484965549760108217304529747*t^2 - 140405140342986489484135310002946668807890609364541485254112518953062149063773107200/31944592128856081147791761663499831484965549760108217304529747*t + 5414044714001540986610493291587210206982928067800831229270622482164355855022668800/31944592128856081147791761663499831484965549760108217304529747
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (70.865902633942745945 - 1.9742410940321862534e-253j)  +/-  (5.1e-119, 5.1e-119j)
| (51.56461200350157768 + 3.3929090481172179277e-252j)  +/-  (2.82e-117, 2.82e-117j)
| (59.939645859977975509 + 3.0146917879834631411e-255j)  +/-  (5.43e-118, 5.43e-118j)
| (44.606518695415751422 + 1.2851188725255381536e-250j)  +/-  (8.9e-117, 8.9e-117j)
| (38.623041671531806385 - 1.5198432008636676531e-258j)  +/-  (1.98e-116, 1.98e-116j)
| (17.643631913869636134 - 1.0582617465963476869e-272j)  +/-  (9.41e-117, 9.41e-117j)
| (33.382672924935195446 + 2.8406596754522924075e-287j)  +/-  (2.62e-116, 2.62e-116j)
| (2.3391552279114836766 - 2.6742167584172252672e-303j)  +/-  (1.67e-121, 1.67e-121j)
| (12.115299911709201361 + 7.8440006706706337353e-297j)  +/-  (1.7e-117, 1.7e-117j)
| (6.0931412788485660358 + 1.5159733324028337501e-305j)  +/-  (3.41e-119, 3.41e-119j)
| (1 + 2.6787247543089674531e-316j)  +/-  (5e-123, 5e-123j)
| (9.8247240235478310543 - 6.3010109914266241689e-310j)  +/-  (5.44e-118, 5.44e-118j)
| (24.6167429055136674 - 2.1360995305423812024e-330j)  +/-  (2.3e-116, 2.3e-116j)
| (20.932363051216429773 - 3.5506006348851407899e-350j)  +/-  (1.69e-116, 1.69e-116j)
| (7.8232631436879996743 - 2.2260985260266951134e-358j)  +/-  (1.57e-118, 1.57e-118j)
| (1.5256036369118887333 - 3.3814952722812078312e-364j)  +/-  (2.63e-122, 2.63e-122j)
| (4.6154961420831741831 - 2.663101865196877745e-363j)  +/-  (6.77e-120, 6.77e-120j)
| (14.71405535563964487 - 7.2767689779537464762e-358j)  +/-  (4.54e-117, 4.54e-117j)
| (28.744969000960047209 + 1.5862463594701388459e-364j)  +/-  (2.9e-116, 2.9e-116j)
| (0.056897625001077184683 + 1.6924156531603179076e-380j)  +/-  (4.59e-127, 4.59e-127j)
| (3.369839231310923141 + 1.1729365612756702425e-374j)  +/-  (1.05e-120, 1.05e-120j)
| (0.66489508742812153521 + 3.3380482885746021206e-378j)  +/-  (6.73e-124, 6.73e-124j)
| (0.29367363028343456214 + 9.3345553866170902123e-380j)  +/-  (2.04e-125, 2.04e-125j)
-------------------------------------------------
The weights are:
| (2.1963281147906688974e-30 - 1.857115730949575927e-276j)  +/-  (4.65e-44, 5.39e-102j)
| (3.0514409375268734936e-22 - 1.3525500815252314957e-271j)  +/-  (2.07e-41, 2.4e-99j)
| (8.6925913685881565351e-26 + 8.1721166808444471697e-274j)  +/-  (9.06e-43, 1.05e-100j)
| (2.724140136107731431e-19 - 1.8708832003233656672e-269j)  +/-  (1.07e-40, 1.24e-98j)
| (9.3993244669906929362e-17 + 1.3568273202491769128e-268j)  +/-  (3.82e-40, 4.43e-98j)
| (6.7510008269602109979e-08 - 2.7309093931841688967e-264j)  +/-  (2.49e-36, 2.89e-94j)
| (1.5634915148844707888e-14 - 1.1690649384610885755e-267j)  +/-  (9.68e-40, 1.12e-97j)
| (0.08923177327727318521 - 2.9698086730879021355e-260j)  +/-  (1.18e-24, 1.37e-82j)
| (1.3366147356568412328e-05 - 5.7141556908237082384e-263j)  +/-  (1.38e-34, 1.6e-92j)
| (0.0036145451678490173702 + 2.1537393139231081268e-261j)  +/-  (2.13e-31, 2.47e-89j)
| (0.13154357347745372878 - 1.097099168531604297e-259j)  +/-  (8.84e-27, 1.03e-84j)
| (0.00011593244361516326845 + 2.1616976744666966057e-262j)  +/-  (9.71e-34, 1.13e-91j)
| (7.9400171663960992962e-11 - 7.5117066090880591009e-266j)  +/-  (2.87e-39, 3.33e-97j)
| (2.8230906173734478882e-09 + 4.8706544194331541848e-265j)  +/-  (2.47e-38, 2.86e-96j)
| (0.00074570751793137916383 - 7.2455559616654822696e-262j)  +/-  (2.69e-34, 3.12e-92j)
| (0.15027699463564965352 + 6.5473163380768977142e-260j)  +/-  (1.28e-30, 1.49e-88j)
| (0.013442730719579223155 - 5.6848876377600895182e-261j)  +/-  (2.79e-33, 3.24e-91j)
| (1.1237623084326404194e-06 + 1.3335305792159373759e-263j)  +/-  (6.2e-37, 7.2e-95j)
| (1.4345550294821630852e-12 + 9.9955982183052674225e-267j)  +/-  (1.4e-40, 1.63e-98j)
| (0.13741771154490287116 + 9.0319503811286192551e-261j)  +/-  (3.83e-33, 4.43e-91j)
| (0.039077977967507132567 + 1.3467702654668172688e-260j)  +/-  (1.57e-33, 1.82e-91j)
| (0.19431274775611323071 + 9.2357632542928669929e-260j)  +/-  (4.95e-33, 5.78e-91j)
| (0.24020574516851107118 - 3.6836794954137458775e-260j)  +/-  (2.69e-33, 3.09e-91j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 3 19
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 19 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^23 + 2967417930088458284793920705351744450134437385517518486007649977219/6516696794286640554149519379353965622932972151062076330124068388*t^22 - 1229686618426373418405591750115990203393835737337757494933291553427943/13033393588573281108299038758707931245865944302124152660248136776*t^21 + 102591227810103949316497086752565608921968483882954472019250772937882693/8688929059048854072199359172471954163910629534749435106832091184*t^20 - 173612109082809906867474056365723517875360088178866561566927453212283977971/173778581180977081443987183449439083278212590694988702136641823680*t^19 + 10537145889916617549701781997203552369445654465051600878473626514879511357131/173778581180977081443987183449439083278212590694988702136641823680*t^18 - 237497270090730416900635635214580080644494865724467564390539510404655088084411/86889290590488540721993591724719541639106295347494351068320911840*t^17 + 477893397154711492415990111444729864325580547974547070816938153349123728473929/5111134740616972983646681866159973037594487961617314768724759520*t^16 - 392797899936864696523841703804651894608851010536452628994840823130909932087858/159722960644280405738958808317499157424827748800541086522648735*t^15 + 1600460976863212326688812048626422191350968169038293617817260290178944009141122/31944592128856081147791761663499831484965549760108217304529747*t^14 - 25328711086719656252436265461345516633898712635390513152076398654462218514654252/31944592128856081147791761663499831484965549760108217304529747*t^13 + 311140239764754145814211126465869055757672202011374697419708713339057930589861684/31944592128856081147791761663499831484965549760108217304529747*t^12 - 2954331488756585760718724027274410445920650081168238517230352536500269781371188712/31944592128856081147791761663499831484965549760108217304529747*t^11 + 21520726336290364407799157769978492804449929427873125388280269122156495469633473128/31944592128856081147791761663499831484965549760108217304529747*t^10 - 118944172133774533134540914678772742514770208562664776294451543727562623650180619280/31944592128856081147791761663499831484965549760108217304529747*t^9 + 491321048218506520362979076129788598651852534638090320010259690746767180492354488880/31944592128856081147791761663499831484965549760108217304529747*t^8 - 1486869467552972877686664738383033467397988598657171894910559856718880343412498223360/31944592128856081147791761663499831484965549760108217304529747*t^7 + 3211786555569535566125012341478532233073901303580665527400932432787726513703557121280/31944592128856081147791761663499831484965549760108217304529747*t^6 - 4784612329546696298890638669805476042044198601658611803314727766542442417807793374720/31944592128856081147791761663499831484965549760108217304529747*t^5 + 4691057769678147436833494847041624642128008839193185156174111957556053821701920371200/31944592128856081147791761663499831484965549760108217304529747*t^4 - 2829565114093491765099781138690384868457822426220384568390613515431222724130491251200/31944592128856081147791761663499831484965549760108217304529747*t^3 + 941963074310698216091183004562275144493158130964800822461570521492641978641151142400/31944592128856081147791761663499831484965549760108217304529747*t^2 - 140405140342986489484135310002946668807890609364541485254112518953062149063773107200/31944592128856081147791761663499831484965549760108217304529747*t + 5414044714001540986610493291587210206982928067800831229270622482164355855022668800/31944592128856081147791761663499831484965549760108217304529747
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   23 out of 23
Indefinite weights: 0 out of 23
Negative weights:   0 out of 23
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (70.865902633942745945 - 1.9742410940321862534e-253j)  +/-  (5.1e-119, 5.1e-119j)
| (51.56461200350157768 + 3.3929090481172179277e-252j)  +/-  (2.82e-117, 2.82e-117j)
| (59.939645859977975509 + 3.0146917879834631411e-255j)  +/-  (5.43e-118, 5.43e-118j)
| (44.606518695415751422 + 1.2851188725255381536e-250j)  +/-  (8.9e-117, 8.9e-117j)
| (38.623041671531806385 - 1.5198432008636676531e-258j)  +/-  (1.98e-116, 1.98e-116j)
| (17.643631913869636134 - 1.0582617465963476869e-272j)  +/-  (9.41e-117, 9.41e-117j)
| (33.382672924935195446 + 2.8406596754522924075e-287j)  +/-  (2.62e-116, 2.62e-116j)
| (2.3391552279114836766 - 2.6742167584172252672e-303j)  +/-  (1.67e-121, 1.67e-121j)
| (12.115299911709201361 + 7.8440006706706337353e-297j)  +/-  (1.7e-117, 1.7e-117j)
| (6.0931412788485660358 + 1.5159733324028337501e-305j)  +/-  (3.41e-119, 3.41e-119j)
| (1 + 2.6787247543089674531e-316j)  +/-  (5e-123, 5e-123j)
| (9.8247240235478310543 - 6.3010109914266241689e-310j)  +/-  (5.44e-118, 5.44e-118j)
| (24.6167429055136674 - 2.1360995305423812024e-330j)  +/-  (2.3e-116, 2.3e-116j)
| (20.932363051216429773 - 3.5506006348851407899e-350j)  +/-  (1.69e-116, 1.69e-116j)
| (7.8232631436879996743 - 2.2260985260266951134e-358j)  +/-  (1.57e-118, 1.57e-118j)
| (1.5256036369118887333 - 3.3814952722812078312e-364j)  +/-  (2.63e-122, 2.63e-122j)
| (4.6154961420831741831 - 2.663101865196877745e-363j)  +/-  (6.77e-120, 6.77e-120j)
| (14.71405535563964487 - 7.2767689779537464762e-358j)  +/-  (4.54e-117, 4.54e-117j)
| (28.744969000960047209 + 1.5862463594701388459e-364j)  +/-  (2.9e-116, 2.9e-116j)
| (0.056897625001077184683 + 1.6924156531603179076e-380j)  +/-  (4.59e-127, 4.59e-127j)
| (3.369839231310923141 + 1.1729365612756702425e-374j)  +/-  (1.05e-120, 1.05e-120j)
| (0.66489508742812153521 + 3.3380482885746021206e-378j)  +/-  (6.73e-124, 6.73e-124j)
| (0.29367363028343456214 + 9.3345553866170902123e-380j)  +/-  (2.04e-125, 2.04e-125j)
-------------------------------------------------
The weights are:
| (2.1963281147906688974e-30 - 1.857115730949575927e-276j)  +/-  (4.65e-44, 5.39e-102j)
| (3.0514409375268734936e-22 - 1.3525500815252314957e-271j)  +/-  (2.07e-41, 2.4e-99j)
| (8.6925913685881565351e-26 + 8.1721166808444471697e-274j)  +/-  (9.06e-43, 1.05e-100j)
| (2.724140136107731431e-19 - 1.8708832003233656672e-269j)  +/-  (1.07e-40, 1.24e-98j)
| (9.3993244669906929362e-17 + 1.3568273202491769128e-268j)  +/-  (3.82e-40, 4.43e-98j)
| (6.7510008269602109979e-08 - 2.7309093931841688967e-264j)  +/-  (2.49e-36, 2.89e-94j)
| (1.5634915148844707888e-14 - 1.1690649384610885755e-267j)  +/-  (9.68e-40, 1.12e-97j)
| (0.08923177327727318521 - 2.9698086730879021355e-260j)  +/-  (1.18e-24, 1.37e-82j)
| (1.3366147356568412328e-05 - 5.7141556908237082384e-263j)  +/-  (1.38e-34, 1.6e-92j)
| (0.0036145451678490173702 + 2.1537393139231081268e-261j)  +/-  (2.13e-31, 2.47e-89j)
| (0.13154357347745372878 - 1.097099168531604297e-259j)  +/-  (8.84e-27, 1.03e-84j)
| (0.00011593244361516326845 + 2.1616976744666966057e-262j)  +/-  (9.71e-34, 1.13e-91j)
| (7.9400171663960992962e-11 - 7.5117066090880591009e-266j)  +/-  (2.87e-39, 3.33e-97j)
| (2.8230906173734478882e-09 + 4.8706544194331541848e-265j)  +/-  (2.47e-38, 2.86e-96j)
| (0.00074570751793137916383 - 7.2455559616654822696e-262j)  +/-  (2.69e-34, 3.12e-92j)
| (0.15027699463564965352 + 6.5473163380768977142e-260j)  +/-  (1.28e-30, 1.49e-88j)
| (0.013442730719579223155 - 5.6848876377600895182e-261j)  +/-  (2.79e-33, 3.24e-91j)
| (1.1237623084326404194e-06 + 1.3335305792159373759e-263j)  +/-  (6.2e-37, 7.2e-95j)
| (1.4345550294821630852e-12 + 9.9955982183052674225e-267j)  +/-  (1.4e-40, 1.63e-98j)
| (0.13741771154490287116 + 9.0319503811286192551e-261j)  +/-  (3.83e-33, 4.43e-91j)
| (0.039077977967507132567 + 1.3467702654668172688e-260j)  +/-  (1.57e-33, 1.82e-91j)
| (0.19431274775611323071 + 9.2357632542928669929e-260j)  +/-  (4.95e-33, 5.78e-91j)
| (0.24020574516851107118 - 3.6836794954137458775e-260j)  +/-  (2.69e-33, 3.09e-91j)
